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  A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs

Hariharan, R., Telikepalli, K., & Mehlhorn, K. (2006). A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs. In Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Part I (pp. 250-261). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-21DE-7 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-21E0-0
Genre: Conference Paper

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 Creators:
Hariharan, Ramesh1, Author           
Telikepalli, Kavitha, Author
Mehlhorn, Kurt1, Author           
Bugliesi, Michele, Editor
Preneel, Bart, Editor
Sassone, Vladimir, Editor
Wegener, Ingo, Editor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph is actually a cycle in the underlying undirected graph with edges traversable in both directions. A {–1,0,1} edge incidence vector is associated with each cycle: edges traversed by the cycle in the right direction get 1 and edges traversed in the opposite direction get -1. The vector space over generated by these vectors is the cycle space of G. A minimum cycle basis is a set of cycles of minimum weight that span the cycle space of G. The current fastest algorithm for computing a minimum cycle basis in a directed graph with m edges and n vertices runs in time (where ω< 2.376 is the exponent of matrix multiplication). Here we present an O(m3n + m2n2logn) algorithm. We also slightly improve the running time of the current fastest randomized algorithm from O(m2nlogn) to O(m2 n + mn2 logn).

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Language(s): eng - English
 Dates: 2007-04-262006
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 314560
Other: Local-ID: C1256428004B93B8-C5345CC3A9361E5BC12571CA003B984B-HTM06a
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Title: Untitled Event
Place of Event: Venice, Italy
Start-/End Date: 2006-07-10

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Title: Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Part I
Source Genre: Proceedings
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Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 250 - 261 Identifier: ISBN: 3-540-35904-4

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Pages: - Volume / Issue: 4051 Sequence Number: - Start / End Page: - Identifier: -